Upward Point-Set Embeddability

We study the problem of Upward Point-Set Embeddability, that is the problem of deciding whether a given upward planar digraph D has an upward planar embedding into a point set S. We show that any switch tree admits an upward planar straight-line embedding into any convex point set. For the class of k-switch trees, that is a generalization of switch trees (according to this definition a switch tree is a 1-switch tree), we show that not every k-switch tree admits an upward planar straightline embedding into any convex point set, for any k 2. Finally we show that the problem of Upward Point-Set Embeddability is NP-complete.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Markus Geyer, Michael Kaufmann, Tamara Mchedlidze, Antonios Symvonis
• Keywords: CORR 2010, Education, Switch Tree, Upward Planar, Upward Planar Digraph